Fuel rod cladding tube for a boiling water reactor fuel rod and the production thereof

ABSTRACT

Cladding tube for a fuel rod for a boiling water reactor fuel element, and its production. The cladding tube is composed practically homogeneously of the constituents of zircaloy and, with the ductility parameter γ= 3 {square root over ((kd))}/(fr) 2 ≦3.5 (γ=ductility parameter, KD=mean grain diameter; fr=Kearns factor), has an elongation at break of at least 20%, set by low-temperature treatment of an extruded tube blank. The starting body used for the extrusion has a defined distribution of precipitated secondary particles which is produced by β-quenching and differs in the areas which form the inner surface and outer surface of the extruded tube. At the inner surface, the particles have a greater diameter and are at a greater average distance apart, this distribution being described by the “spacing”.

BACKGROUND OF THE INVENTION Field of the Invention

The invention relates to a cladding tube for a fuel rod which is or canbe used in a fuel element of a boiling water reactor, the cladding tube,between its inner side (the side facing toward the nuclear fuel enclosedin the cladding tube) (inner surface) and its outer side (outersurface), comprising a zirconium alloy with a practically constantchemical composition, but at these two surfaces having a differentmicrostructure.

Such a fuel rod is illustrated in FIG. 1, in which the two ends of thecladding tube 1 are closed by means of metal stoppers 2 and enclose acolumn of fuel pellets 3. At least at one end (usually the top end), aspring 4 provides a gas collection chamber, while in the stateimmediately after it has been produced, there is a gap 5 between thepellets 3 and the cladding tube 1, which gap closes gradually, however,when the cladding tube is compressed by the pressure of the boilingwater while the reactor is operating and the pellets swell. To ensuregood heat transfer from the pellets to the cladding tube and the coolingwater, the tube generally has a helium atmosphere of a few bar.

FIG. 1 also shows the pellets in the state 3 a immediately after theyhave been produced and in the state 3 b when the reactor has started tooperate and the pellets have burst due to the high thermal loads.

In view of the fundamental requirement that in light water coolednuclear reactors the cladding tubes for the fuel rods should exhibit lowneutron absorption, the cladding tubes are made from a material whichpredominantly comprises zirconium of a purity which is standardized fortubes used in nuclear applications (e.g. R60001). However, in additionto the neutron absorption, a multiplicity of chemical, mechanical andother physical conditions which impose demands on the material and itsproduction have to be observed, and some of these requirements are notcompatible and, moreover, vary for different types of reactor (boilingwater reactor or pressurized water reactor). When used for long periodsin water or steam, pure zirconium is not sufficientlycorrosion-resistant and must therefore be weakly alloyed with additionswhich have to be adapted according to the type of reactor.

Thus, the nuclear reaction causes iodine and other gaseous fissionproducts to be formed in the nuclear fuel, leading, on the one hand, toan increase in volume of the fuel and, on the other hand, to anaggressive atmosphere on the inner side of the cladding tube. The pelletfragments 3 b (FIG. 1) may lead to punctiform pressure and substantiallocal stresses on the inner surface of the cladding tube and, at thesame time, the aggressive fission products are directed onto the innersurface through the fractured surfaces. In zircaloy, which is thestandard material for cladding tubes, this combination of local stressesand an aggressive atmosphere results in stress cracks beginning to formfrom the contact points, along which stress cracks intensified corrosionpropagates, initiated primarily by the iodine. These stress corrosioncracks grow through the entire wall thickness of the cladding tube andlead to perforation of the cladding tube (so-called “pellet claddinginteraction”, PCI).

Pure zirconium (e.g. “sponge zirconium”, which is the standardcommercially available form of reactor-purity zirconium) is lesssusceptible to PCI, since pure zirconium has a higher ductility thanzircaloy, so that the local stresses are partially absorbed by plasticdeformation of the zirconium and are therefore unlikely to reach thethreshold which is critical for PCI. However, pure zirconium is too softin terms of the high mechanical stability required of such claddingtubes (diameter: approx. 1 cm, length approx. 4 m, wall thicknessapprox. 1 mm!). For this reason, so-called “liner cladding tubes”, inwhich a tube made from zircaloy has a thin lining of pure zirconium onthe inner side, are frequently used. Since the introduction of suchliners, punctiform damage caused by PCI is scarcely ever observed on thecorresponding cladding tubes.

Zircaloy is a standardized alloy (e.g. US standard R60802) which has asfar as possible been optimized in terms of stability by the addition oftin and in terms of corrosion by the addition of iron, chromium and, ifappropriate, nickel.

However, PCI damage has been observed practically only in boiling waterfuel elements, but not in pressurized water fuel elements, even thoughthe high pressures in the pressurized water reactor press the claddingtube onto the fuel over the course of time (the so-called “creep”phenomenon). However, the particular way in which boiling water reactorsare controlled results in particularly high loads. The most common causeof damage in pressurized water fuel rods is chemical corrosion from thewater which attacks the outer surface and/or mechanical corrosion causedby friction in the fuel element (so-called “fretting”). In this case,aqueous corrosion acts practically uniformly on the entire surface ofthe cladding tube, which is therefore attacked uniformly (uniformcorrosion), this corrosion behavior being considerably intensified bythe high operating temperature and the chemical composition of thepressurized water in the pressurized water reactor.

Due to the lower operating temperature and the water in the boilingwater reactor containing more oxygen, in practice the corrosion observedon the outer surface of the cladding tubes in such reactors is notuniform, but rather is characterized by punctiform, locally delimitedoxide blisters (so-called “nodular corrosion”), which are not observedin the pressurized water reactor. While individual blisters are oftentolerable, a denser covering with these blisters may lead to deposition(so-called “crud”) of contaminants and dissolved metals (e.g. copper)from the boiling water, an effect which reduces the cooling of the fuelrods and, in extreme cases, uniform corrosion may also be considerablyaccelerated as a result of overheating of the fuel rod.

Nowadays, the cause of the nodular corrosion is considered to be thefact that the alloying elements iron, chromium and nickel are depositedas secondary phases in zirconium alloys, i.e. as particles (“secondaryphase particles”, SPPS) which are distributed throughout the entiregrain structure of the material and the number, size and spacing ofwhich are determined by the manufacturing process. If these SPPs havebecome too large owing to high manufacturing temperatures, they initiatenodular corrosion under the aqueous-chemical conditions of the boilingwater reactor. For this reason, cladding tubes for boiling waterreactors are manufactured in a “low-temperature process” (LTP).

However, advances in reactor engineering have led to the fuel containingever more fissile material, i.e. having a higher energy content, thusallowing a longer service life (so-called “burn-up”) of the fuel rodsand also leading to somewhat higher fuel-rod and operating temperatures.It is therefore necessary even in boiling water reactors to take intoaccount uniform corrosion of the cladding tubes, which according tocurrent knowledge is promoted if the size of the SPPs is too small.Therefore, there is a need for manufacturing processes which allowoptimization between nodular and uniform corrosion.

Further damage to cladding tubes is formed by cracks which have aconsiderable extent in the axial direction. Although these extensivecracks are significantly less common than the PCI defects mentionedabove, they also lead to significantly greater disruptions to operation,since significant quantities of the fuel rod contents can be washed outthrough these cracks. Since these cracks occur considerably more oftenin liner cladding tubes than in liner tubes which consist entirely ofzircaloy (so-called “solid-wall tubes”), there are increasing objectionsto the use of the pure zirconium liner. Moreover, in the case of theliner tubes, it is necessary to ensure, by means of meticulous qualitytesting, that the liner adheres firmly to the supporting tube, so thatthere can be no disruption to the dissipation of heat resulting incorresponding local overheating of the fuel rod.

SUMMARY OF THE INVENTION

The invention is therefore based on the object of providing andproducing a single-component cladding tube which, on the inner surface,has a high resistance to PCI and to the extended cracks mentioned above,which are attributable to embrittlement, and, at the same time, on theouter surface is as resistant as possible both to uniform corrosion andto the nodular corrosion which arises in the cooling water of theboiling water reactor.

The invention works on the basis that the stress-corrosion cracking(induced primarily by iodine), which is largely independent of theprecipitated secondary phases, can be practically prevented by amicrostructure of the matrix in which an optimum grain size is combinedwith an optimum texture. This microstructure is therefore to beapproximately of the same ductility as the iodine-resistant, ductilezirconium liner and, at the same time, is also to be resistant to theextended cracks which are formed in the liner; i.e. it should not bedamaged extensively either by corrosion or by embrittlement.

However, the inner surface should also have a better resistance touniform corrosion than that of pure zirconium, because small amounts ofwater may penetrate through slight defects which in themselves aretolerable (e.g. undiscovered, small leaks in the weld seams or thosebrought about by the “fretting” phenomenon mentioned above) into theinterior of the cladding tube, where this water reacts with the wallmaterial and the fuel so as to evolve oxygen; the oxidation reactionwould be insignificant, but the resultant hydrogen would not be, sinceit would make the wall material brittle. The interaction of oxidationand embrittlement resulting from the uptake of hydrogen may then lead tothe cracks mentioned above.

Therefore, according to EP-A-0,726,966 the pure zirconium of the lineris alloyed with about 0.5% by weight of iron, which is practicallyinsoluble in zirconium. The iron is precipitated in the form ofparticles which increase the resistance to uniform corrosion but onlybring about a slight dispersion hardening, i.e. scarcely change theductility of the pure zirconium.

However, a composite tube of this nature is expensive to produce, sinceit is necessary to avoid the risk of manufacturing errors. Therefore,there is a desire for solutions which allow a material of uniformchemical composition to be used while satisfying the differentrequirements imposed on the two surfaces by means of differences in themicrostructure, i.e. in the grain structure of the alloy matrix and/orthe form and distribution of secondary phases in which insolublealloying fractions are precipitated.

For example, it is proposed in DE-A-29 51 102 for the outer surface of azircaloy cladding tube to undergo secondary heating with laser beams inthe β-area and to be cooled rapidly, in order in that area to establisha quenched β-structure of the matrix with particularly small grains.According to GB-B-1,529,664, a similar effect is achieved by thefinished tube being heated again from the outside, while the innersurface is kept at a lower temperature by means of a flow of water(“temperature gradient annealing”).

According to EP-A-0,660,883, the outer surface is heated into theb-range and is then cooled, but the inner surface is held at amoderately elevated temperature (“partial β-quenching”), water beingatomized onto the inner surface by means of hot inert gas, in order tolimit the temperature gradient during β-quenching. Then, the quenchedβ-structure is present in a relatively wide layer on the outer surface,while the α-structure is present in a thin inner layer which in practiceconstitutes a liner.

According to U.S. Pat. No. 4,718,949, the partial β-quenching can alsobe combined with temperature gradient annealing. In that document, it isproposed for the outer surface of a tube—before or after pilgering stepswhich are used to produce the final dimensions of the tube—to be heatedto the β-range, while the inner surface is being cooled. As a result, toprotect against nodular corrosion, the alloying constituents at theouter surface are to be held predominantly in the matrix and there is tobe less precipitation than on the inner side. Then, the outer surface iscooled and the inner is annealed at the recrystallization temperature inthe α-range. However, these measures require long processing times and ahigh outlay on equipment in order to keep the entire length of thefinished cladding tube in the temperature range required for asufficiently long time, and are therefore not employed.

However, the invention works on the basis that at least the areas on theinner wall, and preferably practically all the areas of the tube wall,should have a high ductility, in order to reduce not only the formation,but also the propagation, of stress cracks. This ductility can beachieved by a matrix of particularly small grains, although largergrains are also possible given a specific structure of the grains, whichcan be described by a relatively high Kearns factor. This leads to theintroduction of a ductility parameter γ=³{square root over((KD))}/(fr)², where (KD) is the mean grain diameter, measured in μm,and (fr) is the Kearns factor. By means of a thermal/mechanicalprocessing which has a virtually uniform action on all parts of the tube(i.e. eliminates temperature gradient annealing), the two variables canbe set in such a way that γ<3.5. This corresponds to an elongation atbreak for the material which is over about 20% at 300° C.

The chemical composition of the material is selected with a view tocorrosion; the composition of zircaloy-2 or zircaloy-4 is particularlysuitable; alternatively, a composition containing the same alloyingconstituents but in concentrations which are optimized so that theydeviate slightly from the standards for zircaloy may also be suitable.As has already been mentioned, the same chemical composition may lead tohigh nodular corrosion and low uniform corrosion or to the oppositescenario if the size and amount of precipitation of undissolved alloyingconstituents (“secondary phases”) are changed by the heat treatmentduring manufacture.

The invention therefore provides for the cladding tube to bemanufactured with a practically homogenous chemical composition, but forthe distribution (size and amount) of secondary phases to be matched tothe requirements imposed on the inner surface and the outer surface bymanufacturing these surfaces from a material which undergoes differentpreliminary heat treatments prior to the abovementionedthermal/mechanical treatment which acts evenly on all areas of thecladding tube and is used to attain the final dimensions of the tube.

This is because the invention provides for the inner surface to have acertain minimum covering of particles of a certain minimum size in orderto protect against uniform corrosion and the cracks mentioned above. Inthis context, however, it is inevitable that particles of this minimumsize will also be formed at the outer surface. The inevitable presenceof large particles on the outer surface is, however, contrary to therequirement in that area that, with regard to nodular corrosion, thesize and number of particles on the outer surface are to be limited.

However, the invention provides a manufacturing process which makes itpossible to produce a cladding tube which fulfills these contradictoryrequirements.

The object set is therefore solved by means of a process and a claddingtube. Advantageous refinements of the invention are described in thesubclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to provide a better understanding of the invention and itsrefinements, an exemplary embodiment is described in more detail withreference to 15 figures, in which:

FIG. 1 shows a longitudinal section through a fuel rod of a boilingwater reactor,

FIG. 2 shows part of the wall of a cladding tube according to theinvention;

FIG. 3 shows a flow diagram for an exemplary embodiment of the processaccording to the invention;

FIG. 4 shows the elongation at break (ductility) of zircaloy claddingtubes with different Q factors, as a function of the particle size ofthe zircaloy;

FIGS. 5, 6 show the cooling-down rate (“CDR”) below the surface and inthe center of a zircaloy body during quenching in water, as a functionof the thickness of the body,

FIGS. 7, 8 show the growth (mean particle diameter φ of the secondaryphases with homogenous annealing and quenching in the center and at thesurface of the body;

FIG. 9 shows the growth of the particles at the inner surface and outersurface of the cladding tube as a function of their fabrication history,

FIGS. 10, 11 show the spacing for particles of larger than 1 μm (innersurface) and larger than 2 μm (outer surface) as a function of theparticle growth parameter or the mean particle size;

FIGS. 12, 13 show the spacing as a function of the level ofprecipitatable alloying constituents for particles of larger than 1 μmand 2 μm, respectively (φ_(g)=1 μm and 2 μm, respectively)

FIG. 14 shows the corrosion as a function of the spacing for φ_(g)=1 μm;

FIG. 15 shows the nodular corrosion as a function of the spacing forφ_(g)=2 μm.

According to the invention, the cladding tube can be produced from astarting body which comprises alloying constituents of zircaloy; thefraction of these constituents which dissolves in the zirconium matrixof the alloy at temperatures of above about 860° C. and is precipitatedas an intermetallic compound (“particles” or “secondary particles”) atlower temperatures, is of particular significance.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The starting body is initially heated to above this dissolutiontemperature, which corresponds to the boundary between the (β+β) phase,and is then cooled, the cooling-down rate being lower in the interior orin a first area of the starting body than in the vicinity of the surface(second area), in which a distribution with smaller and more numerousparticles than in the first area is therefore established.

It is essential that this different distribution should not be destroyedagain by the following further processing, but rather should be largelymaintained. The starting body is therefore extruded but is then nolonger heated to temperatures of over 860° C., but rather only totemperatures of below 810° C., in order to establish particle growthwithout the particles growing to an impermissible size or without adissolution/precipitation process taking place again. Rather, theextrusion produces a tube blank whose inner surface is formed bymaterial of the first area, while the material of the outer surfacecomes from the second area.

By means of a mechanical/thermal treatment (e.g. a pilgering processwith annealing treatments after the individual pilgering steps), theblank is brought to the final dimensions of the cladding tube. In theprocess, a grain structure is established which leads to a ductilitywith a relative elongation at break of at least 20% (measured at 300°C.). The differences in the particle distribution in the various areasof the starting body result in the logarithmic mean of the particle sizeat the inner surface of the cladding tube being greater than at theouter surface.

The surfaces of the corresponding cladding tube therefore consist ofmaterial which comes from areas of a uniformly produced starting bodywhich have been subjected to different heat treatments, and thesesurfaces have different particle distributions and sizes, leading todifferent corrosion behaviors, and can be adapted to the correspondingconditions in the boiling water fuel rod (nodular corrosion on the outersurface; uniform corrosion in the event of water gaining access to theinner surface). In addition, with a view to stress-corrosion cracking, aductility of at least 20% is established and is available even in aniodine-containing atmosphere.

The operating licenses of existing reactors usually work on the basis ofthe standardized alloys zircaloy-2 (1.2 to 1.7% by weight Sn; 0.07 to0.20% by weight Fe; 0.05 to 0.15% by weight Cr and 0.05 to 0.08% byweight Ni) or zircaloy-4 (1.2 to 1.7% by weight Sn; 0.18 to 0.24% byweight Fe; and 0.07 to 0.13% by weight Cr); there is therefore no needto change the license if the invention also complies with these limits.

However, the presence of chromium has proven to be not absolutelynecessary in all cases, while iron contents of up to 0.35% or even 0.4%may be advantageous. In this case, lower limits of 0.05% or at least0.10% Fe may be considered advantageous. Nickel may promote undesiredhydrogenization of the material.

Silicon, like oxygen, is an accompanying element in reactor-purityzirconium which is a permitted contaminant in the standards, but isoften desirable in controlled amounts during production, since the factthat it forms nonmetallic precipitation allows it to be used to goodeffect to set the grain size. Furthermore, up to 0.2% oxygen may beadvantageous, since oxygen improves the mechanical strength withoutsubstantially reducing the ductility.

For corrosion, a minimum tin content of 0.5% was originally considerednecessary with a view to neutralization of nonmetallic and/or disruptiveaccompanying elements, such as nitrogen or phosphorus, but also formechanical properties a minimum tin content of 0.8% is advantageous. Inthis case, it is also possible to use tin contents which lie above thelevels given in the standard, provided that the corrosion-promotinginfluence of larger quantities is compensated for in some other way.However, in combination with a high oxygen content (e.g. more than 0.35%of oxygen +iron), the result could be an excessive hardness of thealloy.

In particular, the invention provides an alloy comprising from 1.0 to2.0% by weight tin, from 0.10 to 0.35% by weight iron, from 0.10 to0.20% by weight chromium, max. 0.10% by weight nickel, from 50 to 200ppm of silicon, remainder zirconium with 0.05 to 0.20% oxygen and otherinevitable accompanying elements and contaminants. Advantageously, thealloy contains, in addition to Zr, Sn, Fe, Cr, Ni, Si and O, only up to0.20% by weight of impurities.

The composition of the cladding tube is practically constant between theinner surface 6 and the outer surface 7 (FIG. 2).

However, the size and number of the particles of the secondary phaseswhich are deposited in the vicinity of these surfaces differ; thesesecondary phases comprise predominantly iron, chromium and/or nickel andtheir intermetallic compounds with zirconium and tin, since Fe, Cr andNi are only very slightly soluble in zirconium. Other contaminants, suchas those which are inevitable in, for example, zirconium and are alsofound in zircaloy, may possibly also form precipitated secondary phasesin some instances, but there has been no evidence of suchsecondary-phase particles having an effect, and this phenomenon istherefore regarded as tolerable. Nevertheless, with a view to unforeseeninfluences, secondary phases of such accompanying elements should as faras possible be avoided or at least be subjected to the same conditions,in terms of size and distribution, as the precipitation of the alloyingconstituents mentioned above.

In a material, the distribution of such particles, the above-mentionedSPPs, can be set by initially heating the material to temperatures atwhich the alloying constituents dissolve. For the constituents mentionedabove, these are temperatures of above about 830° to 860°, i.e. thezirconium alloy is heated into the upper α or the α+β-range. This isthen followed by a controlled heat treatment in which in particular thetimes for which the material is held at temperatures just below thedissolution temperature result in relatively large particles growing atthe expense of the number of small particles precipitated, while lowertemperatures have an ever-decreasing effect on the grain size growth.The inner areas of the cladding tube 2 containing the particles 8therefore come from an area in the starting body which was held athigher temperatures for a longer period (e.g. was cooled more slowly)than the area from which the particles 9 in the outer areas of thecladding tube come.

The effect of this different thermal history is that alloyingconstituents which are not soluble in the cooled matrix of the claddingtube cover less of the inner surface 6 (number of particles per unitarea) than of the outer surface 7, i.e. there is a greater averagedistance between the precipitated particles 8 in the vicinity of theinner surface 6 than between the corresponding particles 9 which aredistributed in the vicinity of the outer surface 7.

Furthermore, FIG. 2 roughly illustrates that the size and texture of thegrains 8′ and 9′ in which the zirconium alloy of the cladding tube isformed are an important factor. This size and texture is virtuallyidentical in all areas of the finished cladding tube.

To produce the cladding tube 2, according to position 10 in the diagramshown in FIG. 3, firstly a melting block made from a zirconium alloy—inthe exemplary embodiment described here containing 1.5% Sn, 0.28% Fe,0.18% Cr, 0.005% Ni, 0.09% O, 0.01% Si, remainder zirconium of standardpurity—is provided as the starting body for manufacture. Compared to thestandard composition of zircaloy, in this alloy the iron and chromiumcontents are selected to be relatively high, and this has a beneficialeffect both on the corrosion resistance and on the hydrogen uptake. Thisconcentration also helps the particles which are precipitated to form inthe desired pattern subsequently.

According to position 11, the melting block is then forged to a diameterof 340 mm at temperatures which initially lie in the Grange and then inthe α-range. Next (position 12), this slab is heated to 1030° C., i.e.to β-temperature.

As the first measure which is of decisive importance for the desiredmicrostructure in the cladding tube, this slab is then quenched in awater bath (position 13). The aim is to maintain a relatively highcooling-down rate at the outer surface when passing through theα+β-range. In the vicinity of the outer surface (for practicalmeasurements, a depth of 5 mm below the outer surface has to be used),this cooling-down rate is at least 30 K/s. However, the center of theslab cools significantly more slowly; the cooling-down rate in thecenter of the slab should not exceed 0.5 K/s. The result is considerabledifferences in the size of the particles which hold the iron, chromiumand nickel which is no longer dissolved in the material. These particlesinitially have a mean diameter of about 15 to 20 mm and grow inproportion to the temperature and time given by the quenching, therelationship being non-linear. In the center of this slab, which is at ahigher temperature for longer than its outer zone, relatively largeparticles are formed.

After this operation, the starting body is then forged again at adefined temperature (position 14). In this example, the temperature is670° C. and the total processing time (including the residence time in afurnace) is 4.5 hours. This heat treatment in the α-range is selected insuch a way that there is a particle growth parameter (PGP) of between0.6 and 1.0, the particle growth parameter—taking into account theheating and cooling-down operations (“cooling-down rate”, CDR, measuredin K/s), which can be estimated at 0.5/CDR, if necessary—being given by

PGP=10¹⁴ ·Σ{t·exp(−Q/nRT)}+0.5/CDR

In this equation, n is a constant (0.47·10⁻⁷) which is typical for thegrowth of particles of this composition, and Q/R is also a constant(18.240 K), so that to determine the PGP, only the time (measured inhours) and temperature (measured in K) used during this heat treatment(position 14) has to be inserted into the following equation

PGP=10¹⁴ ·Σ{t·exp(−32000/T)}+0.5/CDR.

This step can be carried out in such a way that the CDR is of noimportance. The diameter of the billet is now 230 mm. Next, a pipe blankis produced by extrusion (position 15), in that the billet is initiallycut into pieces about 400 mm long, and a hole is drilled in the centerof the pieces which are then extruded at 650° C. The time required forthis manufacturing step is so short that there is no significantparticle growth; i.e. this operation can be disregarded when calculatingthe PGP.

Next, in a plurality of steps 16 and 17, the diameter D is reduced bycertain amounts dD each time, this diameter reduction being broughtabout by cold pilgering with intermediate recrystallization annealingsteps at about 630° C. The individual pilgering steps are carried outwith high levels of deformation, the Q value never falling below 1.0.The recrystallization annealing treatments for all these pilgering stepsamount to total annealing times of 4 hours.

The final forming step (position 18) is cold working by 82%, which iscarried out with a Q value of 6.5 and is concluded by final annealing(position 19) of 6 hours at 560° C.

In general terms, the Q value mentioned is a geometric parameter fordescribing the deformation and is calculated from the wall thicknessS_(o) of the tube prior to pilgering, the wall thickness s afterpilgering, the external diameter D_(o) before pilgering and the externaldiameter D after pilgering, using the following formula$Q = \frac{\ln \quad \left( \frac{s_{0}}{s} \right)}{\ln \quad \left( \frac{D_{0} - s_{0}}{D - s} \right)}$

A further geometric factor is KV, which indicates the cold working inpercent, or the factor y for the logarithmic extension;${{{KV} = {100 \cdot \left\lbrack {1 - \frac{s \cdot \left( {D - s} \right)}{s_{0} \cdot \left( {D_{0} - s_{0}} \right)}} \right\rbrack}};}\quad$$\psi = {{\ln \quad\left\lbrack \frac{s_{0} \cdot \left( {D_{0} - s_{0}} \right)}{s \cdot \left( {D - s} \right)} \right\rbrack} = {\ln \quad\left\lbrack \frac{1}{1 - \frac{Kv}{100}} \right\rbrack}}$

The grain diameter which results after the final forming step isestablished essentially by the extent of cold working. The followingrelationships between the grain diameter KD′ before pilgering and thegrain diameter KD in the pilgered material apply to the pilgering stepsfor the overall working of the pipe blank produced by extrusion(positions 16 to 19):${KD} = {\frac{{KD}^{\prime}}{1 + {\exp \quad \left( {{k_{1} \cdot \psi} - k_{2}} \right)}}.}$

Furthermore, the Kearns factor (fr) is used to describe the crystalorientation, i.e. the position of the crystals (in this case: of thehexagonal crystals) within the grains. This position can in practice beset by the Q factor of the final processing step, although theorientation in the preceding state of the tube also retains aninfluence. The Kearns factor is as follows:

(fr)=(fr)′+k ₃ ·Q.

In the above equations, the constants are as follows: k₁=2.56; k₂=3.66and k₃=0.0182. The Q value, which can be set by means of the way inwhich the process is carried out, therefore provides the possibility ofinfluencing the Kearns factor for the texture. In the example, testsprior to pilgering measured a mean grain diameter KD′=8.7 4 μm and aKearns factor (fr)′=0.55. This results in the following values for thegrain diameter KD of the finished cladding tube: 3.07 μm (measured) and2.83 μm (calculated), and in the following values for the Kearns factor(fr): 0.67 (measured) or 0.67 (calculated). This results, in thefinished cladding tube of the exemplary embodiment, for the ductilityparameter defined in this invention

γ=³ {square root over (KD)}/(fr)²

in the values γ=3.24 (measured) or x=3.15 (calculated), i.e.:

γ≦3.5.

In practice, this relationship applies over the entire volume of thecladding tube, since the size of the grain and the texture of the grainare in practice determined only by measures which have been carried outafter extrusion on the overall tube blank and act evenly on all areas ofthis tube blank. They therefore lead to the same texture and grain sizebeing present on the inner surface as in the other areas of the claddingtube.

FIG. 4 shows how the maximum extension which can be achieved in claddingtubes without fracture under an iodine-containing atmosphere (approx.0.03 mg/cm³) at from 300 to 400° C. is dependent on the grain size KD(iodine stress-cracking test). An elongation at break of 20% is alsofound in pure zirconium, which is used as a liner and can therefore beregarded as providing sufficient protection against PCI andstress-corrosion cracking which starts from the inner surface and iscaused by the iodine-containing medium in the internal volume of thefuel rod. The measured points which lie above the line 20 thereforedescribe a material which is sufficiently resistant to PCI. Thesemeasured points were taken for materials which have been deformed withdifferent Q values. 20′ indicates the materials at the surfaces of thecladding tube according to this exemplary embodiment. The lineapproximately coincides with the boundary condition γ≦3.5. Materialswhich fulfill the condition γ≦3.5 can thus be regarded as beingresistant to PCI.

FIG. 5 plots the cooling-down rate (CDR) which is established at thesurface (curve 21) and in the center (curve 22) of an elongate,cylindrical starting body when the latter is quenched in water and, inthe process, passes through the temperature range between 700ø and 850°C. The cooling-down rate was measured for various diameters M of thematerial. From these curves, it is possible to determine the followingdependency of the cooling-down rate (CDR) on the material thickness M:

CDR=3612·M ^(−1.529) (in the center)

CDR=4.04·M ^(−0.425) (on the outer surface)

For a starting body of M=335 mm, this results, in accordance with theexperiment, in

CDR=0.50 K/s or CDR=34.2 K/s

for the center or about 5 mm below the surface of the starting body,respectively. For M=455 mm, the corresponding values are

CDR=0.31 K/s and CDR=30.1 K/s, respectively.

Both bodies therefore fulfill the condition CDR<0.5 K/s (in the center)and CDR>30 K/s (at the surface). By contrast, thinner or thicker billets(M>455 mm or M<335) are unable to satisfy these conditionssimultaneously.

FIG. 6 shows the cooling-down rate (CDR) in the vicinity of the surface(curve 24) and, in the center (curve 25) of the starting body of thisexemplary embodiment, in a linear/logarithmic representation.

These dimensions of the starting body are fixed in such a way that thePGP and the mean diameter φ of the secondary phases during thecooling-down process adopt the prescribed values both at the surface andin the center simultaneously.

To determine the diameter M of a suitable starting body, the followingrelationship between the mean particle diameter φ (measured in μm) andthe annealing time t (measured in hours) can be used, having been foundby measurements carried out on zircaloy at annealing temperatures ofT=510° C., 630° C., 750° C. and 800° C. (FIG. 7):$\varphi = {\varphi_{\min} + {\frac{\varphi_{\max} - \varphi_{\min}}{1 + \frac{1}{{k \cdot t^{n}}\exp \quad \left( {Q/{RT}} \right)}}\quad {µm}}}$

or, with PGP=PGP=10¹⁴·Σ{t·exp(−Q/nRT)}:$\varphi = {\frac{\varphi_{\min} + {10^{6} \cdot k \cdot {PGP}^{n}}}{\left( {\varphi_{\max} - \varphi_{\min}} \right) + {10^{6} \cdot k \cdot {PGP}^{n}}}\quad {µm}}$

where φ_(min) is the starting value at the beginning of theheat-treatment process (for quenched zircaloy: about 0.02 μm) andφ_(max) is the maximum value which is produced by the insoluble fractionof the alloying elements (in the case of zircaloy: 1.0 μm).

The β-quenching of the starting body causes an increase in the PGP,which can be described by breaking down the temperature range betweenthe dissolution temperature (i.e. the start of precipitation ofsecondary phases, approximately 860° C.) and 700° C. (temperatures lowerthan this make practically no further contribution) into individualsteps and using the end value of the preceding individual step as thestarting value for a following individual step. Tables 1 and 2 and FIG.8 show the results for the material in the center (curve 27) and belowthe surface (curve 26) of the starting body.

The tables also show the development of φ and PGP for the further steps(positions 14 to 19 in FIG. 3), no further growth taking place duringpilgering and cold working. FIG. 9 shows the growth of the particles inthe material which forms the outer surface and inner surface of thefinished cladding tube, i.e. from the peripheral area and center,respectively, of the quenched starting body.

After β-quenching, the following values are found at the inner wall:PGP=1.013 and φ=0.066 μm (Table 1). According to Table 2, the followingvalues apply at the outer surface of the starting body: PGP=0.014, andthe logarithmic mean particle diameter is 0.024 μm.

Hot forging or the temperatures in the α-range result in a change byPGP=0.83, which satisfies the requirement

PGP<1.0.

In the following finishing work carried out on the cladding tube, inpractice only the intermediate annealing and the final annealing(temperatures generally between about 5600 and 630ø) contribute togrowth in particle size and to the grain size, resulting, on both theinner wall and the outer wall, in a PGP=0.18, which complies with thecondition

PGP<0.2

and ultimately in a logarithmic mean of the particle diameter of 0.087μm (at the inner wall) and 0.066 (at the outer wall).

The quenching of the specially dimensioned starting body thereforeproduces, for the precipitated alloying constituents, a desired,extremely differing distribution of coarse and fine particles at theinner and outer surfaces of the cladding tube in those areas of thestarting body from which these surfaces are subsequently forried. Thisis illustrated by curves 28 and 29 from FIG. 9.

As has already been mentioned in the introduction, the inventionprovides for a certain minimum covering of sufficiently large particleson the inner wall (limit value φ_(g) for the individual particle size φ,i.e. a maximum value is to be observed for the distance between thelarge particles (the so-called “spacing” for φ≧φ_(g)) on the inner wall.The spacing can often be measured, but is also given by calculationusing the relationship ${Spacing} = \frac{1000}{\sqrt[3]{N \cdot P}}$

if the total number N of precipitated particles is known, as well as theprobability P(φ_(g)) that one of the particles has a diameter φ which isabove the predetermined limit value φ_(g). The following relationshipapplies to the total number of precipitated particles N$N = {\frac{6\quad \frac{V}{100}}{{\pi \cdot \left( \frac{D}{1000} \right)^{3}}\exp \left\{ {3 \cdot \frac{\ln \quad \left( ɛ^{2} \right)}{2}} \right\}}\quad {mm}^{- 3}}$

where V is the total precipitated volume of alloying constituents(volume of all the precipitated particles), which for zirconiumcontaining 0.16% Fe, 0.11% Cr and 0.06% Ni (i.e. zircaloy-2) is about0.5%. An increase or reduction in the alloying elements changes theprecipitated volume V approximately proportionally, with Ni being ratedat a factor of 3. In this equation, alloying constituents which aresoluble in the matrix, such as for example the metals tin and niobium,and non-metallic elements, such as for example oxygen (likewisesoluble), are not to be taken into account. In the exemplary embodiment,measurements carried out on zircaloy alloys were taken into account andon average gave the same scatter ε=1.93 for all distributions of theprecipitated particles. The basic assumption was a logarithmic standarddistribution, i.e. the diameters φ of the individual particles exhibit adistribution which for log φ′ forms a Gaussian distribution with a meanφ′ and determines the mean particle size φ=exp φ′, and which has a widthwhich results from the standard deviation ε′=log φ−log φ′. Therefore,φ=φ·ε² applies for about 95% of the φ values.

In accordance with this total number N and the mean φ of theprecipitated particles, as well as the scatter ε, the result istherefore a distribution from which the said probability P (φ_(g)) canbe calculated.

For the inner surface, the invention prescribes, for particles whosesize φ reaches at least the limit value φ_(g inner)=1 μm, a maximumspacing of 20 μm, corresponding to a minimum number of 2.5·10³ particlesper mm² or a minimum number of 1.25·10⁵ particles where φ≧φ_(g inner)per mm³ of the volume lying at the inner surface. By contrast, at theouter surface, for particles in which the relationship φ≧φ_(g outer),where φ_(g outer)=2 μm, applies to the individual diameter φ, a maximumspacing of 100 μm is prescribed, corresponding to a maximum number of10² particles per mm² of the outer surface or a maximum number of 10³particles per mm³ of the volume which is distributed at the outersurface.

However, in most cases this means that at the inner surface the meansize of all the particles is higher and their density lower than at theouter surface, as can be seen from FIG. 10.

According to curve 40, to which the right-hand scale belongs, thespacing for particles φ≧1 μm (i.e. the limit value φ_(g) innerprescribed at the inner wall) decreases with increasing PGP′. Curve 41shows the corresponding relationships for φ≧2 μm (i.e. the limit valueφ_(g outer) prescribed at the outer wall). It is assumed here that theparticles are spherical. The particles of the individual diameter φ≧1 μmare to have an average spacing d≧20 μm at the inner wall, whileparticles where φ≧2 μm at the outer wall are to have an average spacingd≧100 μm. This can be reliably achieved if, for example, PGP<1.22 is setat the outer wall, but PGP>1.7 is set at the inner wall.

FIG. 11 shows how these values are converted to the dependency on themean particle size φ. Use is made of the fact that the total number N ofall the precipitated particles is inversely proportional to the 3rdpower of the mean spacing, and the mean particle size can be calculatedfrom the PGP.

The limit value φ_(g)=2 μm and the associated spacing are used tocharacterize a distribution which has a sufficiently small amount ofparticles which are too large and could lead to nodular corrosion at theouter wall. The same distribution, which is characterized by φhd g=2 μmand a spacing of 100 μm, has a spacing of about 75 μm for particles witha minimum size φ_(g)=1.8 μm. With this distribution, the logarithmicmean of the particle size is 0.075 μm. The abovementioned PGP<1.22describes a logarithmic distribution about a mean<0.07 μm, which isassociated with a spacing of>112 μm for φhd g=2 μm and a spacing>85 forφ_(g)=1.8 μm. Accordingly, for PGP=1.7, the mean particle size is about0.08 μm and the spacing is about 18 μm for φ_(g)=1 μm, about 91 μm forφ_(g)=2 μm and about 70 μm for φ_(g)=1.8 μm. According to FIG. 9, φ>0.08μm can be maintained at the inner wall and φ<0.07 μm can be maintainedat the outer wall.

The calculation can also be carried out in the opposite direction:

A spacing which is advantageous with regard to the resistance to nodularcorrosion (the form of corrosion of zircaloy which is encountered underthe chemical/thermal conditions of the boiling water reactor) and is atmost 100 μm is set for the particles at the outer surface of size φ>2μm. The volumetric content of precipitated alloying constituents isdetermined for the alloying composition envisaged. Using these twovariables, it is possible (assuming that the logarithm of the individualparticle sizes φ corresponds to a Gaussian distribution with themeasurable standard deviations which are typical of the alloy) todetermine the mean particle size or the corresponding PGP which, due tothe history, the material has to reach at the outer surface. Thisensures that there are practically no excessively large particles whichcould initiate corrosion at the outer surface.

By contrast, the inner surface is to be protected from uniformcorrosion, which represents a risk on the inner side in the event ofwater penetrating into a defective cladding tube, and is therefore tocontain an adequate number of sufficiently large particles φ>1 μm).

In this connection, the same calculation can be carried out, selecting aspacing which is at least 100 μm and leads to a correspondingly low PGP.The calculation may in this case be replaced by characteristic curvessuch as those which are shown in FIG. 12 for φ_(g)=1 μm and in FIG. 13for φ_(g)=2 μm (i.e. the inner and outer walls).

Since, moreover, a ductility which is similar to that of thetried-and-tested zirconium liner is desired, a thermal/mechanicalpreliminary treatment is fixed in order to set the mean grain diameterKD and the amount of deformation, i.e. the Kearns factor (fr).

Then, the PGP value which corresponds to the growth of the particlesduring the fixed thermal/mechanical preliminary treatment is subtractedfrom the PGP values of the two surfaces. The remaining PGP values forthe material of the outer surface and the inner surface then determinethe sequence which has to be selected for the β-quenching in the centerand at the periphery of the starting body. These cooling-down ratesduring the β-quenching determine the dimensions of the starting bodywhich is to be subjected to the β-quenching. Characteristic curves canalso be calculated and/or measured for this determination of thecooling-down rate and dimensions, as can be seen from FIGS. 5 to 8.

Table 3 shows that elongate, cylindrical starting bodies with diametersM of between 335 mm and 445 mm are in fact suitable for the productionof cladding tubes having the intended particle populations.

For the exemplary embodiment, the data concerning the thermal historyare compiled in Table 4 for the material of the inner wall and of theouter wall, together with the resultant diameters. Table 5 shows datawhich have been measured or calculated on the finished cladding tube.

FIG. 14 relates to the (essentially uniform) corrosion at the innersurface of a zircaloy tube if water has penetrated into the fuel rods.The corrosion rate, i.e. the daily growth in the corrosive layer(measured in mg/dm²) at a test temperature of 350° C., is particularlylow if the spacing for particles of a minimum size φ_(g)=1 μm is about20 μm or below.

By contrast, FIG. 15 describes the corrosion under the conditions whichare encountered at the outer surface of the fuel rod and, in boilingwater reactors, lead to nodular corrosion. The percentage of the surfacearea which is covered by blisters represents a suitable parameter formeasuring nodular corrosion. Even at a test temperature of 500° C., thispercentage is low if the spacing for particles with a minimum sizeφ_(g)=2 μm is over 100 μm, i.e. such particles are only very rare. Inthe meantime, correspondingly fitted fuel rods have been in use in thereactor and to date have presented the advantageous characteristicsexpected.

FIGS. 14 and 15 demonstrate that a greater spacing inhibits nodularcorrosion but promotes uniform corrosion, and therefore in practice itis impossible to simultaneously achieve satisfactory resistance to bothtypes of corrosion. Thus, according to FIG. 14, nodular corrosion is lowwith a spacing of 15 μm, which as shown by FIG. 10 belongs to alogarithmic mean of the particle size of about 0.1 μm; however, as shownin FIG. 10, at this particle size, the spacing at the inner surfaceadopts a value which, as shown by

FIG. 15, leads to a high level of uniform corrosion. The inventiontherefore provides for a particle size at the outer surface which, whensubjected to logarithmic averaging, results in a maximum mean of 0.1 μm,while the particles at the inner surface are at any rate larger onaverage than at the outer surface. Furthermore, irrespective of thedistribution of the particles, the ductility of the wall materialensures that stresses which are initiated by corrosive growth nuclei donot lead to cracks which could propagate in the wall even under aniodine-containing atmosphere.

TABLE 2 FIG. 3 Temp ° C. t (sec.) t (h) PGP Σ PGP φ Pos. 13 850 0.290.003 0.022 (β-Quch.) 840 0.29 0.006 0.023 830 0.29 0.008 0.023 820 0.290.010 0.023 810 0.29 0.011 0.024 800 0.29 0.012 0.024 790 0.29 0.0120.024 780 0.29 0.013 0.024 770 0.29 0.013 0.024 760 0.29 0.014 0.024 7500.29 0.014 0.024 740 0.29 0.014 0.024 730 0.29 0.014 0.024 720 0.290.014 0.024 710 0.29 0.014 0.024 700 0.29 0.014 0.024 14 (Forg.) 670 4.50.828 0.842 0.062 15 (Extr.) 650 180 0.004 0.847 0.062 17 (Recr.) 630 40.164 1.011 0.066 19 (Ann.) 560 6 0.013 1.023 0.066 Final: 1.023 0.066

TABLE 4 Position in Time at temperature PGP FIG. 3 Temp. Outer InnerOuter inner 13 850-700 4.8 s 308 s 0.014 1.013 (Quentch) 34.0 K/s 0.49K/s 14 (Forg.) 670 4.5 h 4.5 h 0.828 0.828 15 (Extr.) 650 180 s 180 s0.004 0.004 17 (Recr.) 630 4 h 4 h 0.164 0.164 19 (Ann.) 560 6 h 6 h0.013 0.013 Final: Σ = 1.023 Σ = 2.022 ↓ ↓ φ_(inner) = φ_(outer) = 0.066μm 0.087 μm

TABLE 3 M = 335 mm M = 445 mm Central Peripheral Central Peripheralβ-Quenching $\begin{matrix}{CDR} & = & {3612\quad \cdot \quad M^{- 1.529}} \\\quad & = & {0.50\quad {K/s}}\end{matrix}$

$\begin{matrix}{CDR} & = & {405\quad \cdot \quad D^{- 0.425}} \\\quad & = & {34.2\quad {K/s}}\end{matrix}$

$\begin{matrix}{CDR} & = & {3612\quad \cdot \quad M^{- 1.529}} \\\quad & = & {0.31\quad {K/s}}\end{matrix}$

$\begin{matrix}{CDR} & = & {405\quad \cdot \quad D^{- 0.425}} \\\quad & = & {30.1\quad {K/s}}\end{matrix}$

${\Delta PGP} = \frac{0.5}{CDR}$

${\Delta PGP} = \frac{0.5}{CDR}$

${\Delta PGP} = \frac{0.5}{CDR}$

${\Delta PGP} = \frac{0.5}{CDR}$

PGP = 1.00 PGP = 0.015 PGP = 1.61 PGP = 0.017 α-Forging PGP = 0.6 . . .1.0 PGP = 0.6 . . . 1.0 PGP = 0.6 . . . 1.0 PGP = 0.6 . . . 1.0Recristall. + PGP = 0.1 . . . 0.2 PGP = 0.1 . . . 0.2 PGP = 0.1 . . .0.2 PGP = 0.1 . . . 0.2 Final Ann. Σ PGP > 1.7 Σ PGP < 1.22 Σ PGP > 2.31Σ PGP < 1.22 Spacing <18.2 μm >112 μm <16 μm >112 μm (φ_(g) = 1 μm)(φ_(g) = 2 μm) (φ_(g) = 1 μm) (φ_(g) = 2 μm)

TABLE 5 measured calculated Mean grain size μm μm 3.07 2.83 Texture(Kearns factor fr) (−) 0.67 0.67 Uniform corrosion (internal) mg/dm²d0.19 Nodular corrosion (external) % 5 Extension in the iodine SCC %22...53 38 test Mean of the SPPs (inner) nm 88 87 Mean of the SPPs(outer) nm 66 66 Spacing (inner) μm 17 Spacing (outer) μm 126 Criterionγ From measured values γ = 3.24 From calculated values γ = 3.15

We claim:
 1. A process for producing a cladding tube for a fuel rod of aboiling water reactor, the method which comprises: heating a startingbody to a given temperature, the starting body being made from alloyingconstituents of a zircaloy, a fraction of the alloying constituentsbeing dissolved at the given temperature, the fraction of the alloyingconstituents being insoluble at an operating temperature of a boilingwater reactor; subsequently cooling a first region of the starting bodyat a first cooling-down rate and cooling a second region of the startingbody at a second cooling-down rate, the first cooling-down rate beingslower than the second cooling-down rate; subsequently extruding thestarting body for forming a tube blank having an inner surface regionand an outer surface region, the outer surface region originating frommaterial of the second region of the starting body having a firstlogarithmic mean value of a particle size of a precipitated fraction ofthe alloying constituents, the inner surface region originating frommaterial of the first region of the starting body having a secondlogarithmic mean value of a particle size of a precipitated fraction ofthe alloying constituents, the first logarithmic mean value being below0.1 μm, the second logarithmic mean value being greater than the firstlogarithmic mean value; producing a cladding tube from the tube blank byusing a mechanical/thermal treatment; exposing the inner surface regionand the outer surface region to substantially identical temperaturesduring the mechanical/thermal treatment and applying, after theextruding step, only temperatures of below 810° C.; providing, with themechanical/thermal treatment, the cladding tube with a given ductility,the given ductility resulting in a ductile yield of at least 20% at atemperature of 300° C.
 2. The process according to claim 1, whichcomprises setting the second logarithmic mean value to be at least 0.01μm greater than the first logarithmic mean value.
 3. The processaccording to claim 1, which comprises setting the first logarithmic meanvalue to be greater than 0.055 μm.
 4. The process according to claim 1,which comprises forging the starting body in an α-range, subsequent tothe cooling step and prior to the extruding step.
 5. A cladding tube fora fuel rod for a boiling water reactor, comprising: a cladding tube bodymade from a starting body by heating the starting body to a giventemperature, the starting body being made from alloying constituents ofa zircaloy, a fraction of the alloying constituents being dissolved atthe given temperature, the fraction of the alloying constituents beinginsoluble at an operating temperature of a boiling water reactor, bysubsequently cooling a first region of the starting body at a firstcooling-down rate and cooling a second region of the starting body at asecond cooling-down rate, the first cooling-down rate being slower thanthe second cooling-down rate, by extruding the starting body to form atube blank having an inner surface region and an outer surface region,said inner surface region originating from material of the first regionof the starting body, said outer surface region originating frommaterial of the second region of the starting body, by heat treating thetube blank using a mechanical/thermal treatment, by exposing the innersurface region and the outer surface region to substantially identicaltemperatures during the mechanical/thermal treatment and by applying,after the extruding, only temperatures of below 810° C.; said claddingtube body having a given ductility with a ductile yield of at least 20%at a temperature of 300° C.; and said cladding tube body having aprecipitated fraction of the alloying constituents with first particlesizes at said outer surface region and second particle sizes at saidinner surface region, said first particle sizes having a firstlogarithmic mean value of less than 0.1 μm, said second particle sizeshaving a second logarithmic mean value being greater than the firstlogarithmic mean value.
 6. The cladding tube according to claim 5,wherein said zircaloy contains from 0.8 to 2.0% by weight of tin, from0.05 to 0.4% by weight of iron, up to 0.20% by weight of chromium and upto 0.15% by weight of nickel.
 7. A cladding tube for a fuel rod for aboiling water reactor, comprising: a cladding tube body including azirconium alloy; said cladding tube body having an inner surface regionand outer surface region, said zirconium alloy extending from said innersurface region to said outer surface region; said inner and outersurface regions being formed from a material originating from givenregions of a starting body having alloying constituents of zircaloy, thegiven regions having been subjected to different heat treatments, afraction of the alloying constituents being insoluble at operatingtemperatures of a boiling water reactor and having a given particle sizedistribution, a logarithmic mean value for a particle size being greaterat said inner surface region than at said outer surface region; and saidcladding tube body having a ductility corresponding to a relativeelongation at break of at least 20% at a temperature of 300° C., theductility being set by mechanical deformation of a tube blank formedfrom the starting body at temperatures below 810° C. and substantiallyidentical at said inner and outer surfaces.
 8. The cladding tubeaccording to claim 7, wherein the logarithmic mean value for theparticle size at said outer surface region is less than 0.1 μm.
 9. Thecladding tube according to claim 7, wherein the logarithmic mean valuefor the particle size at said outer surface region is more than 0.055μm.
 10. The cladding tube according to claim 7, wherein the logarithmicmean value for the particle size at said inner surface region is atleast 0.01 μm greater than the logarithmic mean value for the particlesize at said outer inner surface region.
 11. The cladding tube accordingto claim 7, wherein said zirconium alloy contains from 0.8 to 2.0% byweight of tin, from 0.05 to 0.4% by weight of iron, up to 0.20% byweight of chromium and up to 0.15% by weight of nickel.
 12. A claddingtube for a fuel rod for a boiling water reactor fuel element,comprising: a cladding tube body including a zirconium alloy; saidcladding tube body having an inner surface region and an outer surfaceregion; said zirconium alloy having a substantially constant chemicalcomposition between said inner surface region and said outer surfaceregion and having different microstructures at said inner surface regionand said outer surface region; said zirconium alloy having a grainstructure and texture, at said inner surface region, with a quotient γ=³{square root over ((KD))}/(fr)² of up to 3.5, KD being a mean value of alogarithmic diameter distribution of a grain size measured in μm and frbeing a Kearns parameter; said cladding tube body including precipitatedalloying constituents provided in accordance with a firstthree-dimensional distribution at said inner surface region and providedin accordance with a second three-dimensional distribution at said outersurface region; said precipitated alloying constituents provided inaccordance with the first three-dimensional distribution havingprecipitated particles of a given size, such that if the given sizeexceeds a limit value of 1 μm, an average distance between theprecipitated particles does not exceed 20 μm; and said precipitatedalloying constituents provided in accordance with the secondthree-dimensional distribution having precipitated particles of a givensize such that if the given size exceeds 2 μm, the average distancebetween the precipitated particles is not less than 100 μm.
 13. Thecladding tube according to claim 12, wherein said zirconium alloycontains from 1.0 to 2.0% Sn, from 0.10 to 0.35% by weight Fe, from 0.10to 0.20% by weight Cr, a maximum of 0.10% by weight Ni, and from 50 to200 ppm silicon.
 14. The cladding tube according to claim 12, whereinsaid cladding tube body further includes zirconium including from 0.05to 0.20% oxygen.
 15. The cladding tube according to claim 14, whereinsaid cladding tube body further includes 0.05 to 0.20% oxygen and up to0.20% of other elements.
 16. The cladding tube according to claim 12,wherein said precipitated particles are composed of substantiallyzirconium and at least one of said alloying constituents selected fromthe group consisting of iron, chromium, silicon and nickel.
 17. Aprocess for producing a cladding tube for a fuel element for a boilingwater reactor, the method which comprises: providing a starting bodymade from a zirconium alloy; solution-annealing the starting body at atemperature in a β-range; quenching the starting body with a firstcooling-down rate in a center of the starting body and with a secondcooling-down rate at a depth of 5 mm below an outer surface of thestarting body, the first cooling-down rate, while passing through anα+β-range in the center of the starting body, does not exceed 0.5 K/s,and the second cooling-down rate at a depth of 5 mm below the outersurface is at least 30 K/s; subsequently annealing and forging thestarting body in an α-range and maintaining a value for a particlegrowth parameter of between 0.6 and 1 for a treatment subsequent to thequenching step; and subsequently further processing the starting bodyfor producing a finished cladding tube, the step of further processinghaving a total thermal history resulting in a value of between 0.1 and0.2 for the particle growth parameter.
 18. The process according toclaim 17, which comprises quenching the starting body in a water bath.19. The process according to claim 17, which comprises providing thestarting body with a content of from 1.0 to 2% Sn, from 0.10 to 0.35% byweight Fe, from 0.10 to 0.20% by weight Cr, at most 0.15% by weight Ni,from 50 to 200 ppm of Si, with a remainder of zirconium of standardpurity with from 0.05 to 0.20% by weight O.